The following table is a probability distribution for the random variable x.
| x |
f(x) |
| 5 |
0.10 |
| 20 |
0.60 |
| 35 |
0.30 |
1 The expected value of x is: E(x) = ______.
a 23
b 22
c 21
d 20
2 The variance of x is: var(x) = _______.
a 52
b 81
c 150
d 225
Next 7 questions (3-9) are based on the following:
In the table below x denotes the Z-Lab Company's projected annual profit (in $1,000), along with the probability of earning that profit. The negative value indicates a loss.
| x |
f(x) |
| -50 |
0.10 |
| 0 |
|
| 100 |
0.35 |
| 150 |
0.20 |
| 200 |
0.15 |
| 250 |
0.05 |
3 The probability that Z-Lab will break even, that is, f(x = 0), is,
a 0.30
b 0.25
c 0.20
d 0.15
4 The probability that Z-Lab will be profitable, that is, f(x > 0), is,
a 0.60
b 0.65
c 0.70
d 0.75
5 The mean or expected value of Z-Lab's profit is μ = E(x) = _________.
a $108.3 thousand
b $106.2 thousand
c $102.5 thousand
d $100.8 thousand
6 The variance of profit is var(x) = ________
a 11,180.56
b 6,868.75
c 4,185.25
d 3,942.55
7 On average, each profit (loss) amounts deviate from the mean profit by ______ thousand.
a 115.83
b 105.74
c 82.88
d 76.95
8 Suppose $200 thousand is added to each previously projected profit (loss) level (y = 200 + x), but probabilities are maintained as before. The updated expected value of profit and the variance of profit for Z-Lab, respectively, are:
|
E(y) |
var(y) |
| a |
302.5 |
6,868.75 |
| b |
302.5 |
7,068.75 |
| c |
202.5 |
6,868.75 |
| d |
202.5 |
7,068.75 |
9 Suppose, instead of adding $200 thousand, each profit (and loss) amount is doubled (y = 2x) and probabilities maintained as before. The new expected value of profit and the variance of profit for Z-Lab, respectively, are:
|
E(y) |
var(y) |
| a |
302.5 |
6,868.75 |
| b |
302.5 |
7,068.75 |
| c |
202.5 |
6,868.75 |
| d |
202.5 |
7,068.75 |
Next TWO questions are based on the following:
Bob is a salesman. He receives 20% of the price of the item sold as sales commission plus a fixed salary of $400 per week. Bob's average weekly sales is 15 items with a standard deviation of 5. The average price of items Bob sells is $250. Bob works 46 weeks a year.
10 Bob's average annual earnings is ________.
a $49,600
b $50,700
c $51,800
d $52,900
11 In the previous question, what is the standard deviation of the annual salary?
a $12,100
b $11,500
c $10,900
d $10,300
Next FOUR questions (12-15) are based on the following:
Consider a binomial experiment with n = 10 and π = 0.45. Let x denote the number of successes.
12 f(x = 4) = _______.
a 0.3173
b 0.2884
c 0.2622
d 0.2384
13 f(x ≤ 3) = _______ f(x ≥ 3) = _______
a 0.2660 0.7340
b 0.2394 0.8104
c 0.2660 0.9004
d 0.2394 0.7606
14 E(x) = ______.
a 6
b 5.5
c 5
d 4.5
15 var(x) = ______.
a 2.950
b 2.825
c 2.645
d 2.475
16 Suppose you are receiving a large shipment of Gizmos. The manufacturing standards provide that 1% of Gizmos turn out defective. You randomly select a sample of n = 50 from each lot and return the shipment if more than 2 are found defective. The probability of returning a shipment is:
a 0.0894
b 0.0358
c 0.0138
d 0.0016
17 A comprehensive test has 50 multiple questions. Each question has 5 choices. The test score is assigned from the scale of 100. That is, each question is worth 2 points. If you guessed the answers for all 50 questions, what is the expected score?
a 10
b 15
c 20
d 25
Next three questions are based on the following:
John is a speed demon. The probability that he will get a speeding ticket while driving to and from work is 30 percent. Answer the next three questions based on a work week (n = 5).
18 What is the probability that John will get 2 tickets during the week (Monday-Friday)?
a 0.3087
b 0.3364
c 0.3441
d 0.3717
19 What is the probability that John will get at least one ticket during the work week?
a 0.8985
b 0.8319
c 0.2496
d 0.1681
20 If each ticket costs John $180 what is the average cost of speeding violation in the 5-day period?
a $260
b $270
c $280
d $290.